I'd recommend buying the ABA Guide to Southeast Arizona. It will help you choose the birding sites you'd like to visit. From there, choose where to stay.
There are three places to stay in Madera Canyon: Santa Rita Lodge, Madera Kubo cabins, and The Chuparosa Inn (B&B). They're right in the thick of things.
Sierra Vista is a likely stop, and all of the chain hotels are there. There are also birder's beds-and-breakfast in the area, as well as the cabins at Beatty's Orchard (a must-stop for hummingbirds) in Miller Canyon.
The American Birding Association puts out a monthly newsletter, "Winging It." It has ads for several of the B&Bs.
As for the Chiricahua Mountains (my favorite), there are several places to stay: The Portal Peak Lodge, Cave Creek Ranch, the George Walker House (in Paradise, about five miles from Portal), and a few others. I've stayed at Portal Peak Lodge and Cave Creek Ranch and would recommend either.
Camping is an option in all the mountain ranges: the Santa Ritas, the Huachucas, and the Chiricahuas.
The three big tour companies in the US (Wings, Field Guides, Victor Emanuel Nature Tours), along with several others, offer guided trips to this area, usually in winter and in late July/early August. Once the monsoon season starts (often around July 4th), the desert temperatures abate somewhat (we birded in the 70-80-degree range often last July), and hummingbird diversity is at its peak.
There are several very good birding guides who live/work in these areas, and some advertise in "Winging It."
Hope this helps. I find it best to put together a trip by choosing the target birds, then working toward a set of destinations/sleeping accommodations that best fits getting the targets. In general, birders who go to SE Arizona hit all three mountain ranges in a big loop.
If you'd like any more information, I'd be happy to help. SE AZ is one of my favorite places in the world, and well worth the trip for any birder/naturalist.
Steve in Houston